Single-electron multiplication statistics as a combination of poissonian pulse height distributions using constraint regression methods

Abstract

Analysing the histogram of anode pulse amplitudes allows a discussion of the hypothesis that has been proposed to account for the statistical processes of secondary multiplication in a photomultiplier. In an earlier work, we obtained good agreement between experimental and reconstructed spectra, assuming a first dynode distribution including two Poisson distributions of distinct mean values. This first approximation led us to look for a method which could give the weights of several Poisson distributions of distinct mean values. We have briefly exposed three methods: classical linear regression, constraint regression (d'Esopo's method), and regression on variables subject to error. The use of these methods gives us an approach of the frequency function which represents the dispersion of the punctual mean gain around the whole first dynode mean gain value. Comparison between this function and the one employed in Polya distribution allows us to state that the latter is inadequate to describe the statistical process of secondary multiplication. We have analysed numerous spectra obtained with two kinds of photomultiplier working under different physical conditions. Then we discuss two points: - Does the frequency function represent the dynode structure and the interdynode collection process? - Is our model (the multiplication process of all dynodes but the first one, is Poissonian) valid whatever the photomultiplier and the utilization conditions?